The transition to a global hydrogen economy necessitates the development and optimization of technologies for hydrogen production, storage, and utilization, many of which operate under supercritical conditions. Accurate prediction of the thermodynamic properties of supercritical hydrogen is therefore of paramount importance for engineering design, operational efficiency, and safety. This review provides a critical evaluation and comparative analysis of two dominant classes of thermodynamic models: The computationally simple cubic equations of state (CEoSs), such as Peng–Robinson and Soave–Redlich–Kwong, and the more physically rigorous statistical associating fluid theory (SAFT)-based models. The analysis reveals that classical CEoSs exhibit significant inaccuracies in predicting the properties of supercritical hydrogen, a failure rooted in their empirical formulation, which cannot account for the quantum mechanical effects prominent in light fluids. In contrast, SAFT-based models, which are derived from molecular-level principles, demonstrate consistently superior accuracy in predicting volumetric, caloric, and transport-related properties across wide ranges of temperature and pressure. This review elucidates the fundamental reasons for these performance disparities and discusses the practical trade-offs between model simplicity and predictive power. Future research directions are explored, including the role of quantum corrections for cubic models, the development of hybrid EoSs, and the transformative potential of machine learning for EoS parameterization and property prediction.